Optical solitons provide unique opportunities for the control of light‐bylight. Today, the field of soliton formation in natural materials is mature, as the main properties of the possible soliton states are well understood. In particular, optical solitons have been observed experimentally in a variety of materials and physical settings, including media with cubic, quadratic, photorefractive, saturable, nonlocal and thermal nonlinearities. New opportunities for soliton generation, stability and control may become accessible in complex engineered, artificial materials, whose properties can be modified at will by, e.g., modulations of the material parameters or the application gain and absorption landscapes. In this way one may construct different types of linear and nonlinear optical lattices by transverse shallow modulations of the linear refractive index and the nonlinearity coefficient or complex amplifying structures in dissipative nonlinear media. The exploration of the existence, stability and dynamical properties of conservative and dissipative solitons in settings with spatially inhomogeneous linear refractive index, nonlinearity, gain or absorption, is the subject of this PhD Thesis. We address stable conservative fundamental and multipole solitons in complex engineered materials with an inhomogeneous linear refractive index and nonlinearity. We show that stable two‐dimensional solitons may exist in nonlinear lattices with transversally alternating domains with cubic and saturable nonlinearities. We consider multicomponent solitons in engineered materials, where one field component feels the modulation of the refractive index or nonlinearity while the other component propagates as in a uniform nonlinear medium. We study whether the cross‐phase‐modulation between two components allows the stabilization of the whole soliton state. Media with defocusing nonlinearity growing rapidly from the center to the periphery is another example of a complex engineered material. We study such systems and, in contrast to the common belief, we have found that stable bright solitons do exist when defocusing nonlinearity grows towards the periphery rapidly enough. We consider different nonlinearity landscapes and analyze the types of soliton solution available in each case. Nonlinear materials with complex spatial distributions of gain and losses also provide important opportunities for the generation of stable one‐ and multidimensional fundamental, multipole, and vortex solitons. We study onedimensional solitons in focusing and defocusing nonlinear dissipative materials with single‐ and double‐well absorption landscapes. In two‐dimensional geometries, stable vortex solitons and complexes of vortices could be observed. We not only address stationary vortex structures, but also steadily rotating vortex solitons with azimuthally modulated intensity distributions in radially symmetric gain landscapes. Finally, we study the possibility of forming stable topological light bullets in focusing nonlinear media with inhomogeneous gain landscapes and uniform twophoton absorption.

The field of nonlinear optics, which has undergone a very rapid development since the discovery of lasers in the early sixties, continues to be an active and rapidly developing - search area. The interest is mainly due to the potential applications of nonlinear optics: - rectly in telecommunications for high rate data transmission, image processing and recognition or indirectly from the possibility of obtaining large wavelength range tuneable lasers for applications in industry, medicine, biology, data storage and retrieval, etc. New phenomena and materials continue to appear regularly, renewing the field. This has proven to be especially true over the last five years. New materials such as organics have been developed with very large second- and third-order nonlinear optical responses. Imp- tant developments in the areas of photorefractivity, all optical phenomena, frequency conv- sion and electro-optics have been observed. In parallel, a number of new phenomena have been reported, some of them challenging the previously held concepts. For example, solitons based on second-order nonlinearities have been observed in photorefractive materials and frequency doubling crystals, destroying the perception that third order nonlinearities are - quired for their generation and propagation. New ways of creating and manipulating nonl- ear optical materials have been developed. An example is the creation of highly nonlinear (second-order active) polymers by static electric field, photo-assisted or all-optical poling. Nonlinear optics involves, by definition, the product of electromagnetic fields. As a con- quence, it leads to the beam control.

Describing progress achieved in the field of nonlinear optics and nonlinear optical materials, the Handbook treats selected topics such as photorefractive materials, third-order nonlinear optical materials and organic nonlinear optical crystals, as well as electro-optic polymers. Applications of photorefractive materials in optical memories, optical processing, and guided-wave nonlinear optics in hotorefractive waveguides are described. As light will play a more and more dominant role as an information carrier, the review of existing and new materials given here makes this a keystone book in the field.

The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain. Drawing on the award winning research of Carnegie Mellon’s David S. Ricketts, Electrical Solitons Theory, Design, and Applications is the first text to focus specifically on KdV solitons in the nonlinear transmission line. Divided into three parts, the book begins with the foundational theory for KdV solitons, presents the core underlying mathematics of solitons, and describes the solution to the KdV equation and the basic properties of that solution, including collision behaviors and amplitude-dependent velocity. It also examines the conservation laws of the KdV for loss-less and lossy systems. The second part describes the KdV soliton in the context of the NLTL. It derives the lattice equation for solitons on the NLTL and shows the connection with the KdV equation as well as the governing equations for a lossy NLTL. Detailing the transformation between KdV theory and what we measure on the oscilloscope, the book demonstrates many of the key properties of solitons, including the inverse scattering method and soliton damping. The final part highlights practical applications such as sharp pulse formation and edge sharpening for high speed metrology as well as high frequency generation via NLTL harmonics. It describes challenges to realizing a robust soliton oscillator and the stability mechanisms necessary, and introduces three prototypes of the circular soliton oscillator using discrete and integrated platforms.

Nonlinear photonics is the name given to the use of nonlinear optical devices for the generation, communication, processing, or analysis of information. This book is a progress report on research into practical applications of such devices. At present, modulation, switching, routing, decision-making, and detection in photonic systems are all done with electronics and linear optoelectronic devices. However, this may soon change, as nonlinear optical devices, e.g. picosecond samplers and switches, begin to complement optoelectonic devices. The authors succinctly summarize past accomplishments in this field and point to hopes for the future, making this an ideal book for newcomers or seasoned researchers wanting to design and perfect nonlinear optical devices and to identify applications in photonic systems.

It is ironic that the ideas ofNewton, which described a beam of light as a stream ofparticles made it difficult for him to explain things like thin film interference. Yet these particles, called 'photons', have caused the adjective 'photonic' to gain common usage, when referring to optical phenomena. The purist might argue that only when we are confronted by the particle nature of light should we use the word photonics. Equally, the argument goes on, only when we are face-to face with an integrable system, i. e. one that possesses an infinite number of conserved quantities, should we say soliton rather than solitary wave. Scientists and engineers are pragmatic, however, and they are happy to use the word 'soliton' to describe what appears to be an excitation that is humped, multi humped, or localised long enough for some use to be made of it. The fact that such 'solitons' may stick to each other (fuse) upon collision is often something to celebrate for an application, rather than just evidence that, after all, these are not really solitons, in the classic sense. 'Soliton', therefore, is a widely used term with the qualification that we are constantly looking out for deviant behaviour that draws our attention to its solitary wave character. In the same spirit, 'photonics' is a useful generic cover-all noun, even when 'electromagnetic theory' or 'optics' would suffice.

This book introduces the basic concept of a dissipative soliton, before going to explore recent theoretical and experimental results for various classes of dissipative optical solitons, high-energy dissipative solitons and their applications, and mode-locked fiber lasers. A soliton is a concept which describes various physical phenomena ranging from solitary waves forming on water to ultrashort optical pulses propagating in an optical fiber. While solitons are usually attributed to integrability, in recent years the notion of a soliton has been extended to various systems which are not necessarily integrable. Until now, the main emphasis has been given to well-known conservative soliton systems, but new avenues of inquiry were opened when physicists realized that solitary waves did indeed exist in a wide range of non-integrable and non-conservative systems leading to the concept of so-called dissipative optical solitons. Dissipative optical solitons have many unique properties which differ from those of their conservative counterparts. For example, except for very few cases, they form zero-parameter families and their properties are completely determined by the external parameters of the optical system. They can exist indefinitely in time, as long as these parameters stay constant. These features of dissipative solitons are highly desirable for several applications, such as in-line regeneration of optical data streams and generation of stable trains of laser pulses by mode-locked cavities.

This textbook is an introduction to the theory of solitons in the physical sciences.